Method and device for estimating movement parameters of targets

ABSTRACT

A method of providing parameter values which pertain to the relative kinematic behavior of an object ( 10 ), in particular a first vehicle ( 10 ), and a target object ( 12 ), in particular a second vehicle ( 12 ), a conclusion being able to be drawn on the basis of the parameter values as to whether the object ( 10 ) and the target object ( 12 ) will probably collide, using the steps:  
     a) providing a sensor system ( 11 ) on the object ( 10 ), the sensor system ( 11 ) being provided for transmitting and receiving signals to determine measured values r i , v r,i  for target object distance r and/or for relative radial velocity v r  between the object ( 10 ) and the target object ( 12 ),  
     b) determining measured values r i , v r,i  and  
     c) analyzing measured values r i , v r,i  thus determined and providing the parameter values.  
     Step c) is implementable on the basis of signals received by a receiver.  
     A device for outputting parameter values is also described.

[0001] The present invention relates to a method of providing parameter values pertaining to the relative kinematic behavior of an object, in particular a first vehicle, and a target object, in particular a second vehicle, a conclusion being reached on the basis of these parameter values as to whether the object and the target object will presumably collide. This method includes the following steps:

[0002] a) providing a sensor system on the object, the sensor system being provided for transmitting and receiving signals in order to detect measured values r_(i), v_(r,i) for target object distance r and/or for relative radial velocity v_(r) of the target object,

[0003] b) determining measured values r_(i), v_(r,i) and

[0004] c) analyzing measured values r_(i), v_(r,i) thus determined and providing the parameter values.

[0005] The present invention also relates to a device for outputting parameter values pertaining to the relative kinematic behavior of an object, in particular a first vehicle, and a target object, in particular a second vehicle, so that on the basis of these parameter values, it is possible to reach a conclusion as to whether the object and the target object will presumably collide. This device has a sensor system arranged on the object, the sensor system being provided to transmit and receive signals, to determine measured values r_(i), v_(r,i) for target object distance r and/or relative radial velocity v_(r) of the target object, and means for analyzing measured values r_(i), v_(r,i) determined by the sensor system and outputting the parameter values.

BACKGROUND INFORMATION

[0006] In the field of automotive engineering, for example, methods of providing and/or devices for outputting parameter values which pertain to and/or describe the relative kinematic behavior of a first vehicle and a second vehicle and/or any obstacle are necessary in order to reach a conclusion regarding a possible collision or to detect a dead angle with the help of these parameter values. To this end, sensors such as optical sensors, capacitive sensors, ultrasonic sensors or radar sensors are used to measure distance r between the vehicles, and/or relative radial velocity v_(r) of the second vehicle within a range to be monitored. It is known that by differentiation of the radial velocity, the radial component of relative radial acceleration a_(r) of the second vehicle may be determined from these measured values. In addition, it is also known that the radial velocity may be determined, for example, by analyzing the Doppler frequency or by differentiation of the distance. According to the related art, the normal components of the distance, of the velocity, and of the acceleration perpendicular to the front area of the vehicle may be calculated by triangulation from the measured values of several spatially distributed sensors. For triangulation, it is thus necessary to have multiple transmitting and/or receiving units and/or sensors distributed spatially, and this entails high hardware costs. Another problem occurring with the related art is that even when using multiple sensors, under some circumstances only one sensor will receive a signal suitable for analysis. In this case triangulation cannot be performed, so an imminent collision cannot be detected.

ADVANTAGES OF THE INVENTION

[0007] Due to the fact that step c) of the method according to the present invention is implementable on the basis of signals received by only one receiver, i.e., no triangulation is performed, the hardware cost may be reduced and reliable predictions may be made even if only one sensor receives a signal suitable for use for a corresponding analysis.

[0008] The same thing is also true of the device according to the present invention in which the means perform the analysis on the basis of the signals received by only one receiver assigned to the sensor system.

[0009] The following embodiments are based on the method according to the present invention as well as the device according to the present invention.

[0010] Without constituting a restriction, the parameter values preferably pertain to one or more of the following parameters: the relative acceleration a of the target object, relative velocity v of the target object, relative radial velocity v_(r) of the target object, offset Δy between the object and the target object, angle α between the vectors of the relative velocity v of the target object and relative radial velocity v_(r) of the target object i.e., between the vectors of relative acceleration a of the target object and relative radial acceleration a_(r) of the target object. The parameter values for some of these parameters are preferably estimated on the basis of the available measured values, and the parameter values for other parameters are determined on the basis of the estimated parameter values.

[0011] To this end, a vector {right arrow over (p)} is preferably used, containing at least some of the parameters being sought, this vector {right arrow over (p)} optionally having the form

{right arrow over (p)}=[a, v₀, α₀

[0012] where a denotes the relative acceleration of the target object, v₀ denotes the relative initial velocity of the target object in the first measurement in the first repetition, and α₀ is the angle between the vectors of relative velocity v of the target object and relative radial velocity v_(r) of the target object, i.e., the angle between the vectors of relative acceleration a of the target object and relative radial acceleration a_(r) of the target object in the first measurement. The first measurement refers to the first measurement of a plurality of measurements performed at different points in time t_(i), where i=1, 2, . . . . Points in time t_(i) may be equidistant but need not be. For example, measured values at equidistant target distances may also be detected.

[0013] According to a first embodiment of the present invention, target object distances r_(i) are measured at different points in time t_(i) and target object distance r is described by the equation

r=f({right arrow over (p)},t)={square root}{square root over ((r ₀ cos(α₀)+v ₀ t+at ²/2)²+(r ₀ sin(α₀))²)}

[0014] where r₀ is the target object distance in the first measurement, v₀ is the relative initial velocity of the target object in the first measurement in the first repetition, a is the relative acceleration of the target object, t is the time and α₀ is the angle between the vectors of relative velocity v of the target object and relative radial velocity v_(r) of the target object, i.e., the angle between the vectors of relative acceleration a of the target object and relative radial acceleration a_(r) of the target object in the first measurement.

[0015] In particular, in this embodiment, the parameter values for the parameters contained in vector {right arrow over (p)} may be estimated on the basis of a norm to be explained in greater detail below. For the sake of simplicity, the estimation may also be performed with the help of values t_(i), r_(i) ² after squaring the equation given above.

[0016] According to a second embodiment of the present invention, relative radial velocities V_(r,i) are measured at different points in time t_(i), and relative radial velocity v_(r) of the target object is described by the equation: $v_{r} = {{f\left( {\overset{\rightarrow}{p},t} \right)} = \frac{\left( {v_{0} + {at}} \right)\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)}{\sqrt{\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)^{2} + \left( {r_{0}{\sin \left( \alpha_{0} \right)}} \right)^{2}}}}$

[0017] Parameters r₀, v₀, a, t and α₀ correspond to the parameters of the first embodiment.

[0018] According to a third embodiment of the present invention, target object distances r_(i) and relative radial velocities of v_(r,i) are measured at different points in time t_(i) and relative radial velocity v_(r) of the target object is described by the equation: $v_{r} = {{f\left( {\overset{\rightarrow}{p},t,r} \right)} = \frac{\left( {v_{0} + {at}} \right)\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right.}{r}}$

[0019] Here again, parameters r₀, v₀, a, t and α₀ correspond to the parameters in the first embodiment.

[0020] The embodiments just described may optionally be combined in a suitable manner or reformulated mathematically.

[0021] The norm theory on which the following discussion is based will be familiar to those skilled in the art. For details, reference is made to G. Grosche, V. Ziegler, D. Ziegler: Supplementary chapter to I. N. Bronstein, K. A. Semendjajew, Taschenbuch der Mathematik Handbook of Mathematics, 6^(th) edition, B. G. Teubner, Verlagsgesellschaft Leipzig, 1979.

[0022] To estimate the parameter values, preferably a norm Q({right arrow over (p)}) is defined a follows in conjunction with the first embodiment:

Q({right arrow over (p)})=Q ₁({right arrow over (p)})=∥r _(i) ^(k) −f ^(k)({right arrow over (p)}, t _(i))∥, where k=1 or k=2

[0023] where k=1 or k=2.

[0024] An example of the definition of norm Q({right arrow over (p)}) may have the following form in conjunction with the first embodiment: ${{Q\left( \overset{\rightarrow}{p} \right)} = {{Q_{11}\left( \overset{\rightarrow}{p} \right)} = {\sum\limits_{i}^{\quad}\quad \left( {r_{i}^{k} - {f^{k}\left( {\overset{\rightarrow}{p},t_{i}} \right)}} \right)^{2}}}},{{{where}\quad k} = {{1\quad {or}\quad k} = 2}}$

[0025] where k=1 or k=2.

[0026] Another example of the definition of the norm Q({right arrow over (p)}) may provide the following form in conjunction with the first embodiment:

Q({right arrow over (p)})=Q ₁₂({right arrow over (p)})=max(|r _(i) ^(k) −f ^(k)({right arrow over (p)}, t _(i))|), where k=1 or k=2

[0027] where k=1 or k=2.

[0028] To estimate the parameter values, preferably a norm Q({right arrow over (p)}) is defined as follows in conjunction with the second embodiment:

Q({right arrow over (p)})=Q ₂({right arrow over (p)})=∥v _(i) ^(k) −f ^(k)({right arrow over (p)}, t _(i))∥, where k=1 or k=2

[0029] where k=1 or k=2.

[0030] An example of the definition of the norm Q({right arrow over (p)}) may provide the following form in conjunction with the second embodiment: ${{Q\left( \overset{\rightarrow}{p} \right)} = {{Q_{21}\left( \overset{\rightarrow}{p} \right)} = {\sum\limits_{i}^{\quad}\quad \left( {v_{i}^{k} - {f^{k}\left( {\overset{\rightarrow}{p},t_{i}} \right)}} \right)^{2}}}},{{{where}\quad k} = {{1\quad {or}\quad k} = 2}}$

[0031] where k=1 or k=2.

[0032] Another example of the definition of norm Q({right arrow over (p)}) may provide the following form in conjunction with the second embodiment:

Q({right arrow over (p)})=Q ₂₂({right arrow over (p)})=max(|v _(i) ^(k) −f ^(k)({right arrow over (p)}, t _(i))|), where k=1 or k=2

[0033] where k=1 or k=2.

[0034] To estimate the parameter values, preferably a norm Q({right arrow over (p)}) is defined as follows in conjunction with the third embodiment:

Q({right arrow over (p)})=Q ₃({right arrow over (p)})=v_(i) ^(k) −f ^(k)({right arrow over (p)}, t _(i) , r _(i))∥, where k=1 or k=2.

[0035] where k=1 or k 2.

[0036] An example of the definition of the norm Q({right arrow over (p)}) may provide the following form in conjunction with the third embodiment: ${{Q\left( \overset{\rightarrow}{p} \right)} = {{Q_{31}\left( \overset{\rightarrow}{p} \right)} = {\sum\limits_{i}^{\quad}\quad \left( {v_{i}^{k} - {f^{k}\left( {\overset{\rightarrow}{p},t_{i},r_{i}} \right)}} \right)^{2}}}},{{{where}\quad k} = {{1\quad {or}\quad k} = 2}}$

[0037] where k=1 or k=2.

[0038] Another example of the definition of the norm Q({right arrow over (p)}) may provide the following form in conjunction with the third embodiment.

Q({right arrow over (p)})=Q ₃₂({right arrow over (p)})=max(|v _(i) ^(k) −f ^(k)({right arrow over (p)}, t _(i) , r _(i))|), where k=1 or k=2

[0039] where k=1 or k=2.

[0040] As mentioned above, the parameter values for the parameters contained in vector {right arrow over (p)} are preferably estimated on the basis of the measured values.

[0041] In this connection, it is preferable for the parameter values for the parameters contained in vector {right arrow over (p)} to be estimated on the basis of an optimization method using points in time t_(i) and measured values r_(i) for the target object distance and/or measured values v_(r,i) for the relative radial velocity of the target object; this is done by determining the minimum of the norm Q({right arrow over (p)}).

[0042] A suitable optimization method which may be used, for example, when the norm Q({right arrow over (p)}) has the form ${{Q\left( \overset{\rightarrow}{p} \right)} = {{Q_{11}\left( \overset{\rightarrow}{p} \right)} = {\sum\limits_{i}^{\quad}\quad \left( {r_{i}^{k} - {f^{k}\left( {\overset{\rightarrow}{p},t_{i}} \right)}} \right)^{2}}}},{{{where}\quad k} = {{1\quad {or}\quad k} = 2}},{or}$ ${{Q\left( \overset{\rightarrow}{p} \right)} = {{Q_{21}\left( \overset{\rightarrow}{p} \right)} = {\sum\limits_{i}^{\quad}\quad \left( {v_{i}^{k} - {f^{k}\left( {\overset{\rightarrow}{p},t_{i}} \right)}} \right)^{2}}}},{{{where}\quad k} = {{1\quad {or}\quad k} = 2}},{or}$ ${{Q\left( \overset{\rightarrow}{p} \right)} = {{Q_{31}\left( \overset{\rightarrow}{p} \right)} = {\sum\limits_{i}^{\quad}\quad \left( {v_{i}^{k} - {f^{k}\left( {\overset{\rightarrow}{p},t_{i},r_{i}} \right)}} \right)^{2}}}},{{{where}\quad k} = {{1\quad {or}\quad k} = 2}}$

[0043] is the method of least error squares, which is well known to those skilled in the art.

[0044] In some cases, it may be assumed for the sake of simplicity that relative acceleration a of the target object is constant and/or that acceleration vector {overscore (a)} is parallel to velocity vector {overscore (v)}. Accordingly, then a linear variation of relative velocity v of the target object is assumed. In this connection, for example, it is possible to assume that the relative acceleration is a=0 m/s². In addition, it may be assumed that the relative velocity amounts to a=0 m/s² when relative velocity v is greater than a predetermined limiting value, and the relative acceleration is a=0 m/s2 when relative velocity v is less than the previously determined limiting value.

[0045] When the estimated parameter values for the parameters contained in vector {right arrow over (p)} are available, offset Δy between the object and the target object may be determined on the basis of the equation

Δy=r ₀ sin(α₀.

[0046] In addition, instantaneous angle α(t) between the vectors of relative velocity v of the target object and relative radial velocity v_(r) of the target object, i.e., between the vectors of relative acceleration a of the target object and relative radial acceleration a_(r) of the target object may be determined from the estimated parameter values of the parameters contained in vector {right arrow over (p)} and offset Δy between the object and the target object by using the equation ${\alpha (t)} = {{{atan}\left( \frac{\Delta \quad y}{{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)}.}$

[0047] It is also possible to determine the relative instantaneous velocity v(t) of the target object by using the estimated parameter values of the parameters contained in vector {right arrow over (p)} on the basis of the equation

v(t)=v ₀ +at.

[0048] The absolute value of the relative instantaneous radial velocity of the target object may be determined from the estimated parameter values of the parameters contained in vector {right arrow over (p)} by using the equation

|v _(r)(t)|=|(v ₀ +at)cos(α)|.

[0049] When an angle between a normal of the object and the vector of target object distance r is equal to angle between the vectors of relative velocity v of the target object and relative radial velocity v_(r) of the target object or between the vectors of relative acceleration a of the target object and relative radial acceleration a_(r) of the target object, then the normal component relative to the object is v_(n)=v, a_(n)=a and x=r cos(α). In this case, time t₁ of a collision which may take place is determined from the estimated parameter values of the parameters contained in vector {right arrow over (p)} by using the equation $t_{1} = {\frac{- \sqrt{v_{0}^{2} - {2r_{0}a\quad {\cos \left( \alpha_{0} \right)}}}}{a} - \frac{v_{0}}{a}}$

[0050] When one vehicle drives by another, t₁ is the point in time having the shortest target distance at point P.

[0051] In addition it is possible for an error factor e({right arrow over (p)}) to be defined using the estimated parameter values of the parameters contained in vector {right arrow over (p)} by using the equation:

e ₁({right arrow over (p)})=∥r ^(k) _(i) −f ^(k)(p,t _(i))∥, where k=1 or k=2, or

e ₂({right arrow over (p)})=∥v ^(k) _(i) −f ^(k)(p,t _(i))∥, where k=1 or k=2, or

e ₃({right arrow over (p)})=∥v ^(k) _(i) −f ^(k)(p,t _(i),r_(i))∥, where k=1 or k=2

[0052] Error factor e({right arrow over (p)}) is provided to perform an error estimate for the estimated parameter values and/or for the parameter values derived from the estimated parameter values. Error factor e({right arrow over (p)}) also makes it possible to define threshold values which may be adapted to the respective application, for example. When values are above or below these threshold values, the parameter values may be classified as invalid for individual parameters, for example.

[0053] Any device suitable or implementation of the method according to the present invention falls within the scope of the respective claims.

[0054] With regard the means provided with the device according to the present invention, it should be pointed out that these means may easily be implemented by those skilled in the art through the use of suitable hardware or software or other circuits.

DRAWING

[0055] The present invention is explained in greater detail below on the basis of the respective drawings.

[0056]FIG. 1 shows a geometric representation of the object and the target object.

[0057]FIG. 2 shows a representation of the various parameters.

DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS

[0058]FIG. 1 shows an object in the form of a first vehicle, labeled on the whole with reference number 10. A sensor system is situated on first vehicle 10. The normal to the front area of first vehicle 10 is labeled as 13. A target object in the form of a second vehicle is labeled on the whole with reference number 12. On the whole, FIG. 1 illustrates the case of one vehicle driving by another, i.e., there is no collision. The distance between first vehicle 10 and second vehicle 12 is characterized by a vector r whose component normal to the front area of first vehicle 10 is labeled as x. An angle β is formed between vectors r and x. When second vehicle is at point P, the offset between first vehicle 10 and second vehicle 12 is Δy, the initial distance between point P and second vehicle 12 being characterized by vector z.

[0059] On the basis of offset Δy, it is possible to detect either that the vehicle will pass by or that a collision is imminent. Offset Δy is in this case assumed to lie in the horizontal plane (azimuth). It is expedient here to measure with a small angle in the vertical direction (elevation). For example, if the height of the target object, i.e., the offset in the vertical direction, is to be determined, then a small angle in the azimuth is suitable. In principle, measurement of the offset in a plane with any desired inclination to the horizontal or vertical plane is also possible by using a suitably shallow antenna diagram. If the offset is measured in two planes orthogonal to one another (e.g., elevation and azimuth), then the target coordinates in the space monitored are determined unambiguously by target object distance r.

[0060]FIG. 2 illustrates a few important parameters. The initial position of first vehicle 10 and of second vehicle 12 corresponds to that in FIG. 1. The vector arrows in FIG. 2 indicate the kinematic behavior of second vehicle 12. In practice, however, both first vehicle 10 and second vehicle 12 are moving or the target object is not a second vehicle but instead is a stationary target object. Therefore, relative variables are referred to here as were in the preceding discussion.

[0061] Vectors v_(r) and a_(r) denote the relative radial velocity and the radial acceleration, respectively of second vehicle 12. Vectors v and a denote the relative velocity and relative acceleration, respectively, of second vehicle 12, an angle α being formed between vectors v_(r) and v, i.e., a_(r) and a. The tangential components of relative radial velocity v_(r) perpendicular to the radial component or relative radial acceleration a_(r) of the second vehicle are given as v_(t) and a_(t), respectively, point P being defined by vectors v, and a_(t) or v and a.

[0062] The preceding description of exemplary embodiments of the present invention is presented only for the sake of illustration and is not intended to restrict the scope of the present invention. Various changes and modifications are possible within the scope of the present invention without going beyond the scope of the present invention or its equivalents. 

What is claimed is:
 1. A method of providing parameter values which pertain to the relative kinematic behavior of an object (10), in particular a first vehicle (10), and a target object (12), in particular a second vehicle (12), a conclusion being able to be drawn on the basis of the parameter values as to whether the object (10) and the target object (12) will probably collide, having the steps: a) providing a sensor system (11) on the object (10), the sensor system (11) being provided for transmitting and receiving signals to determine measured values r_(i), v_(r,i) for target object distance r and/or for relative radial velocity v_(r) of the target object (12), b) determining measured values r_(i), v_(r,i) and c) analyzing measured values r_(i), v_(r,i) thus determined and providing the parameter values, wherein step c) is implementable on the basis of signals received by a receiver.
 2. The method according to claim 1, wherein the parameter values pertain to at least one or more of the following parameters: relative acceleration a of the target object (12), relative radial acceleration a_(r) of the target object (12), relative velocity v of the target object (12), relative radial velocity v_(r) of the target object (12), offset Δy between the object (10) and the target object (12), angle α between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12) i.e., between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12).
 3. The method according to claim 1 or 2, wherein a vector {right arrow over (p)} is provided containing at least some of the parameters being sought, this vector {right arrow over (p)} having the form {right arrow over (p)}=[a, v₀, α₀ where a denotes the relative acceleration of the target object (12), v₀ denotes the relative initial velocity of the target object (12) in the first measurement, and α₀ denotes the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 4. The method according to one of the preceding claims, wherein in step b) target object distances r_(i) are measured at different points in time t_(i) and target object distance r is described by the equation: r=f({right arrow over (p)},t)={square root}{square root over ((r ₀ cos(α₀)+v ₀ t+at ²/2)²+(r ₀ sin(α₀))²)} where r₀ denotes the target object distance in the first measurement, v₀ denotes the relative initial velocity of the target object (12) in the first measurement, a denotes the relative acceleration of the target object (12), t is the time and α₀ is the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 5. The method according to one of the preceding claims, wherein in step b) relative radial velocities v_(r,i) of the target object (12) are measured at different points in time time t_(i) and relative radial velocity v_(r) of the target object (12) is described by the equation: $v_{r} = {{f\left( {\overset{\rightarrow}{p},t} \right)} = \frac{\left( {v_{0} + {at}} \right)\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)}{\sqrt{\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)^{2} + \left( {r_{0}{\sin \left( \alpha_{0} \right)}} \right)^{2}}}}$

where r₀ denotes the target object distance in the first measurement, v₀ denotes the relative initial velocity of the target object (12) in the first measurement, a denotes the relative acceleration of the target object (12), t is the time and α₀ is the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 6. The method according to one of the preceding claims, wherein in step b) target object distances r_(i) and relative radial velocities v_(r,i) are measured at different points in time t_(i) and relative radial velocity v_(r) of the target object (12) is described by the equation: $v_{r} = {{f\left( {\overset{\rightarrow}{p},t,r} \right)} = \frac{\left( {v_{0} + {at}} \right)\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right.}{r}}$

where r₀ denotes to target object distance in the first measurement, v₀ denotes the relative initial velocity of the target object (12) in the first measurement, a denotes the relative acceleration of the target object (12), t is the time and α₀ is the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 7. The method according to one of the preceding claims, wherein for estimation of the parameter values, a norm Q({right arrow over (p)}) is defined as follows: Q({right arrow over (p)})=Q₁({right arrow over (p)})=∥r _(i) ^(k) −f ^(k)({right arrow over (p)},t _(i))∥, where k=1 or k=2, or Q({right arrow over (p)})=Q ₂({right arrow over (p)})=∥v _(i) ^(k) −f ^(k)({right arrow over (p)},t _(i))∥, where k=1 or k=2, or Q({right arrow over (p)})=Q ₃({right arrow over (p)})=∥v _(i) ^(k) −f ^(k)({right arrow over (p)},t _(i) ,r _(i))∥, where k=1 or k=2.
 8. The method according to one of the preceding claims, wherein the parameter values for the parameters contained in vector {right arrow over (p)} are estimated on the basis of the measured values.
 9. The method according to one of the preceding claims, wherein the parameter values for the parameters contained in vector {right arrow over (p)} are estimated on the basis of the points in time t_(i) and measured values r_(i) for the target object distances and/or measured values v_(i) for the relative radial velocities by using an optimization method by determining the minimum of the norm Q({right arrow over (p)}).
 10. A device for outputting parameter values which pertain to the relative kinematic behavior of an object (10), in particular of a first vehicle (10), and a target object (12), in particular a second vehicle (12), a conclusion optionally being able to be drawn on the basis of the parameter values as to whether the object (10) and the target object (12) will probably collide, having: a sensor system (11) situated on the object (10), the sensor system (11) being provided for transmitting and receiving signals in order to determine measured values r_(i), v_(r,i) for target object distance r and/or for relative radial velocity v_(r) of the target object (12), and means for analyzing the measured values r_(i), v_(r,i) determined by the sensor system and for outputting the parameter values, wherein the means perform the analysis on the basis of signals received by only one of the receivers assigned to the sensor system (11).
 11. The device according to claim 10, wherein the parameter values pertain to at least one or more of the following parameters: relative acceleration a of the target object (12), relative radial acceleration a_(r) of the target object (12), relative velocity v of the target object (12), relative radial velocity v_(r) of the target object (12), offset Δy between the object (10) and the target object (12), angle α₀ between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12).
 12. The device according to claim 10 or claim 11, wherein a vector {right arrow over (p)} is provided for analyzing measured values r_(i), v_(r,i) detected by the sensor system (11), this vector containing at least some of the parameters being sought, the vector {right arrow over (p)} having the form {right arrow over (p)}=[a, v₀,α₀ where a denotes the relative acceleration of the target object (12), v₀ denotes the relative initial velocity of the target object (12) in the first measurement and α₀ denotes the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 13. The device according to one of claims 10 through 12, wherein the sensor system (11) detects measured values for target object distances r_(i) at different points in time t_(i) and the means describe target object distance r on the basis of the equation: r=f({right arrow over (p)},t)={square root}{square root over ((r ₀ cos(α₀)+v ₀ t+at ²/2)²+(r ₀ sin(α₀))²)} where r₀ denotes the target object distance in the first measurement, v₀ denotes the relative initial velocity of the target object (12) in the first measurement, a denotes the relative acceleration of the target object (12), t is the time and α₀ is the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 14. The device according to one of claims 10 through 13, wherein the sensor system (11) detects measured values for relative radial velocities v_(r,i) of the target object (12) at different points in time t_(i), and the means describe relative radial velocity v_(r) of the target object (12) by using the equation: $v_{r} = {{f\left( {\overset{->}{p},t} \right)} = \frac{\left( {v_{0} + {at}} \right)\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)}{\sqrt{\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)^{2} + \left( {r_{0}{\sin \left( \alpha_{0} \right)}} \right)^{2}}}}$

where r₀ denotes the target object distance in the first measurement, v₀ denotes the relative initial velocity of the target object (12) in the first measurement, a denotes the relative acceleration of the target object (12), t is the time and α₀ is the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 15. The device according to one of claims 10 through 14, wherein the sensor system (11) detects measured values for target object distances r_(i) and measured values for relative radial velocities v_(r,i) at different points in time t_(i), and the means describe relative radial velocity v_(r) of the target object (12) by using the equation: $v_{r} = {{f\left( {\overset{->}{p},t,r} \right)} = \frac{\left( {v_{0} + {at}} \right)\left( {{r_{0}{\cos \left( \alpha_{0} \right)}} + {v_{0}t} + {{at}^{2}/2}} \right)}{r}}$

where r₀ denotes the target object distance in the first measurement, v₀ denotes the relative initial velocity of the target object (12) in the first measurement, a denotes the relative acceleration of the target object (12), t is the time and α₀ is the angle between the vectors of relative velocity v of the target object (12) and relative radial velocity v_(r) of the target object (12), i.e., the angle between the vectors of relative acceleration a of the target object (12) and relative radial acceleration a_(r) of the target object (12) in the first measurement.
 16. The device according to one of claims 10 through 15, wherein the means for estimating the parameter values define a norm Q({right arrow over (p)}) as follows: Q({right arrow over (p)})=Q₁({right arrow over (p)})=∥r _(i) ^(k) −f ^(k)({right arrow over (p)},t _(i))∥, where k=1 or k=2, or Q({right arrow over (p)})=Q ₂({right arrow over (p)})=∥v _(i) ^(k) −f ^(k)({right arrow over (p)},t _(i))∥, where k=1 or k=2, or Q({right arrow over (p)})=Q ₃({right arrow over (p)})=∥v _(i) ^(k) −f ^(k)({right arrow over (p)},t _(i) ,r _(i))∥, where k=1 or k=2.
 17. The device according to one of claims 10 through 16, wherein the means estimate the parameter values for the parameters contained in vector {right arrow over (p)} on the basis of the measured values.
 18. The device according to one of claims 10 through 17, wherein the means estimate the parameter values for the parameters contained in vector {right arrow over (p)} on the basis of points in time t_(i) and measured values r_(i) for the target object distances and/or measured values v_(i) for the relative radial velocities by using an optimization method in which they determine the minimum of the norm Q({right arrow over (p)}). 